{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Математическая статистика\n",
    "## Практикум 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as sps\n",
    "import ipywidgets as widgets\n",
    "import matplotlib.pyplot as plt\n",
    "import random as rd\n",
    "from collections import Counter\n",
    "from collections import OrderedDict\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Укажем вариант и считаем все необходимые значения по заданному варианту группы."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Номер варианта</th>\n",
       "      <th>Трансцендентная функция</th>\n",
       "      <th>Полином</th>\n",
       "      <th>Показатель a для Гамма-распределения</th>\n",
       "      <th>Показатель scale для Гамма-распределения</th>\n",
       "      <th>Показатель \\mu_1 для нормального распределения</th>\n",
       "      <th>Показатель \\sigma_1 для нормального распределения</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>14</td>\n",
       "      <td>ln(5x)</td>\n",
       "      <td>4x^2+3x-2</td>\n",
       "      <td>4.650034</td>\n",
       "      <td>3.432432</td>\n",
       "      <td>2.532169</td>\n",
       "      <td>4.733873</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Номер варианта Трансцендентная функция    Полином   \n",
       "14              14                  ln(5x)  4x^2+3x-2  \\\n",
       "\n",
       "    Показатель a для Гамма-распределения   \n",
       "14                              4.650034  \\\n",
       "\n",
       "    Показатель scale для Гамма-распределения   \n",
       "14                                  3.432432  \\\n",
       "\n",
       "    Показатель \\mu_1 для нормального распределения   \n",
       "14                                        2.532169  \\\n",
       "\n",
       "    Показатель \\sigma_1 для нормального распределения  \n",
       "14                                           4.733873  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 14\n",
    "# достаем входные данные\n",
    "data = pd.read_excel('datasets/application_to_practicum2.xlsx').loc[[N]]\n",
    "o = 10 ** -5 # маленькое число, исключительно для удобства\n",
    "\n",
    "# функция для преобразования текста в валидный код\n",
    "def as_function(function):\n",
    "    return function\\\n",
    "        .replace('^', '**')\\\n",
    "        .replace('x', '*x')\\\n",
    "        .replace('ln', 'np.log')\\\n",
    "        .replace('sin', 'np.sin')\\\n",
    "        .replace('cos', 'np.cos')\\\n",
    "        .replace('tan', 'np.tan')\\\n",
    "        .replace('exp', 'np.exp')\\\n",
    "        .replace('arctan', 'np.arctan')\n",
    "        \n",
    "# достаем нужные нам параметры\n",
    "transcendental_function = as_function(data['Трансцендентная функция'].item())\n",
    "polynomial = as_function(data['Полином'].item())\n",
    "gamma_a = data['Показатель a для Гамма-распределения'].item()\n",
    "gamma_scale = data['Показатель scale для Гамма-распределения'].item()\n",
    "μ = data['Показатель \\mu_1 для нормального распределения'].item()\n",
    "σ = data['Показатель \\sigma_1 для нормального распределения'].item()\n",
    "\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сделаем функцию $\\chi^2$ с выравниванием чисел чтобы не было ошибке о большой разнице"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def chisquare(expected, real):\n",
    "    mapped = np.array(expected) * np.mean(real) / np.mean(expected) # трюк чтобы убрать отклонение \n",
    "    return sps.chisquare(f_exp = mapped, f_obs = real)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сделаем функцию для преобразования набора случайных величин в плотность распределения путем дискретезации"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def digitize(distribution, bin_count):\n",
    "    bins = np.linspace(min(distribution), max(distribution), num = bin_count)\n",
    "    \n",
    "    counter = Counter(np.digitize(distribution, bins))\n",
    "    oredered = OrderedDict(sorted(counter.items(), key = lambda t: t[0]))\n",
    "    \n",
    "    data = dict.fromkeys(bins, 0)\n",
    "    \n",
    "    for key, count in oredered.items():\n",
    "        data[bins[key - 1]] = count\n",
    "        \n",
    "    sample = np.array(list(data.values()))\n",
    "    return data.keys(), sample / np.sum(sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сделаем функцию для проверки $p-value$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_p_value(actual, critical):\n",
    "    if actual >= critical:\n",
    "        print(f'Нет оснований отвергать гипотезу, p-value = {actual}')\n",
    "    else:\n",
    "        print (f'Гипотеза о равномерности отвергается')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Смоделировать выборку объема $n=1000$ из распределения Бернулли $Bin(1,p)$, где $p$ соответствует таблице и вашему номеру варианта (приложение 1 к Практикуму2).\n",
    "Проверить с помощью $\\chi^2$ на соответствие данных теоретической модели."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>1. Теоретическая модель</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 1 / N\n",
    "n = 1000\n",
    "bin_count = 20\n",
    "binom = sps.binom(n, p)\n",
    "\n",
    "x = np.arange(\n",
    "    binom.ppf(o),\n",
    "    binom.ppf(1 - o)\n",
    ")\n",
    "theory_binom = binom.pmf(x)\n",
    "\n",
    "plt.plot(x, theory_binom)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>2. Моделирование</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = []\n",
    "\n",
    "for i in range(n):\n",
    "    sample.append(sps.bernoulli.rvs(p, size = n).sum()) # выборка возвращает 0 1 0, поэтому считаем единицы\n",
    "\n",
    "keys, practical_binom = digitize(sample, bin_count)\n",
    "    \n",
    "plt.plot(keys, practical_binom)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>3. Соответсвие моделей с $\\chi^2$</strong>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Проведем $\\chi^2$ тест, на соответствие данных теоретической модели."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Power_divergenceResult(statistic=6.786266306905371, pvalue=0.9952688308379387)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theory_sized = []\n",
    "\n",
    "for i in range(len(practical_binom)): # преобразуем эксперементальные данные в более узкий размер наблюдаемых\n",
    "    index = int(len(theory_binom) / len(practical_binom) * i)\n",
    "    theory_sized.append(theory_binom[index])\n",
    "\n",
    "chisquare(theory_sized, practical_binom)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$p-value > 0.05$, значит мы не можем отбросить гипотезу о их соответствии"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача 2\n",
    "\n",
    "Создать  таблицы 100 значений для одной трансцендентной и одной рациональной функции (из приложения 1) в соответствии со своим вариантом. Используя эту таблицу выписать 100 цифр, выбирая из каждого значения функции  второй знак справа от запятой. Для полученной выборки проверить по критерию $\\chi^2$ гипотезу о равновероятности получить любую цифру на втором месте после запятой, при уровне значимости 0.01."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_second_or_zero(x):\n",
    "    return int(x * 100) % 10\n",
    "\n",
    "def to_second_digits(array):\n",
    "    digits_collected = list(map(lambda x: get_second_or_zero(x), array))\n",
    "    digits_count = {}\n",
    "\n",
    "    for i in range(len(set(digits_collected))):\n",
    "        digits_count[i] = digits_collected.count(i)\n",
    "        \n",
    "    return digits_count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Делаем эталонный массив с равномерным распределением цифр"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = [10] * 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сделаем функцию для проверки гипотезы о равновероятности получить любую цифру при уровне значимости 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check(sample):\n",
    "    check_p_value(\n",
    "        actual = chisquare(digits, list(sample)).pvalue, \n",
    "        critical = 0.01\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>1. Создаем словари</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "transcendental_function_table = {}\n",
    "polynomial_table = {}\n",
    "\n",
    "N = 100\n",
    "\n",
    "for i in range(1, N + 1):\n",
    "    x = i / N # делаем так, чтобы были дробные числа, по возрастанию, чтобы потом не сортировать лишний раз\n",
    "    transcendental_function_table[x] = eval(transcendental_function) # чтобы можно было решить любой вариант\n",
    "    polynomial_table[x] = eval(polynomial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>2. Трансцендентная функция</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Нет оснований отвергать гипотезу, p-value = 0.0314974175867212\n",
      "Цифра: Количество\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{0: 12, 1: 13, 2: 8, 3: 11, 4: 9, 5: 8, 6: 9, 7: 9, 8: 9, 9: 12}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(transcendental_function_table.keys(), transcendental_function_table.values(), label = transcendental_function)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "digits_count = to_second_digits(list(transcendental_function_table.values()))\n",
    "check(digits_count)\n",
    "\n",
    "print('Цифра: Количество')\n",
    "digits_count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<strong>3. Рациональная функция</strong>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Нет оснований отвергать гипотезу, p-value = 0.0314974175867212\n",
      "Цифра: Количество\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{0: 10, 1: 9, 2: 8, 3: 13, 4: 14, 5: 6, 6: 15, 7: 11, 8: 7, 9: 7}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(polynomial_table.keys(), polynomial_table.values(), label = polynomial)\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "digits_count = to_second_digits(list(polynomial_table.values()))\n",
    "check(digits_count)\n",
    "\n",
    "print('Цифра: Количество')\n",
    "digits_count"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача 3\n",
    "\n",
    "Смоделировать первую выборку $X_n$ гамма-распределения с  показателями $a, scale$ (из приложения 1 в соотвтествии с вашим вариантом) объемом 100.\n",
    "А также вторую выборку $Y_n=X_n+\\varepsilon_n$, где $\\varepsilon_n$ моделирует ошибку измерения и само является \n",
    "выборкой объема 100 нормального распределения со средним $\\mu=0$ и отклонением $\\sigma=scale/4$.  Проверить критерием Колмогорова-Смирнова (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kstest.html) гипотезу о том, что выборка $X_n $ согласуется с гипотезой о $ \\Gamma$-распределении, и что выборки  $X_n$ и $Y_n$ однородны, то есть принадлежат одному распределению."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Нет оснований отвергать гипотезу, p-value = 0.08105771161340149\n",
      "Gamma распределение: KstestResult(statistic=0.4, pvalue=0.08105771161340149, statistic_location=0.05944816249631337, statistic_sign=-1)\n",
      "Нет оснований отвергать гипотезу, p-value = 0.469506448503778\n",
      "Выборки X и Y однородны: KstestResult(statistic=0.12, pvalue=0.469506448503778, statistic_location=13.293976793933043, statistic_sign=1)\n"
     ]
    }
   ],
   "source": [
    "N = 100\n",
    "𝜎 = gamma_scale / 4\n",
    "bin_size = 20\n",
    "\n",
    "gamma_distribution = sps.gamma.rvs(gamma_a, scale = gamma_scale, size = N)\n",
    "norm_distribution = sps.norm.rvs(np.sqrt(𝜇), 𝜎, size = N)\n",
    "\n",
    "x = np.linspace(sps.gamma.ppf(o, gamma_a), sps.gamma.ppf(1 - o, gamma_a), bin_size)\n",
    "gamma_pdf = sps.gamma.pdf(x, gamma_a, scale = gamma_scale)\n",
    "\n",
    "keys, practical_gamma = digitize(gamma_distribution, bin_size)\n",
    "\n",
    "plt.plot(x, gamma_pdf)\n",
    "plt.plot(keys, practical_gamma)\n",
    "plt.show()\n",
    "\n",
    "def kstest(message, first, second):\n",
    "    result = sps.kstest(first, second)\n",
    "    check_p_value(actual = result.pvalue, critical = 0.05)\n",
    "    print(f'{message}: {result}')\n",
    "\n",
    "kstest('Gamma распределение', practical_gamma, gamma_pdf)\n",
    "kstest('Выборки X и Y однородны', gamma_distribution, gamma_distribution + norm_distribution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задача 4\n",
    "\n",
    "Смоделировать выборку вида $X_n+\\varepsilon_n$, где $X_n$-распределено нормально с  показателями $\\mu_1$ и отклонением $\\sigma_1$ (из приложения 1 в соотвтествии с вашим вариантом), $\\varepsilon_n$ моделирует \n",
    "ошибку измерения и само является \n",
    "выборкой нормального распределения со средним $\\mu_2=0$ и отклонением $\\sigma_2$. Протестировать на нормальность полученную выборку.\n",
    "\n",
    "Проиллюстрировать графически зависимость результатов тестирования от объема выборки при $\\sigma_2=\\sigma_1/i$, где i пробегает множество натуральных чисел меньших 20.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "При пороге p-value в 0.8, 1 из 20\\\n",
      "    нулевых гипотез о нормальности полученного распределения не отвергнуто\n"
     ]
    }
   ],
   "source": [
    "N = 2000\n",
    "norm_x = sps.norm.rvs(𝜇, 𝜎, size = N)\n",
    "size = 20\n",
    "bin_count = 10\n",
    "critical = 0.8\n",
    "\n",
    "kstest_result = []\n",
    "debug = False\n",
    "\n",
    "for i in range(1, size + 1):\n",
    "    norm_e = sps.norm.rvs(0, 𝜎 / i, size = N)\n",
    "    \n",
    "    keys_x, values_x = digitize(norm_x, bin_count = bin_count)\n",
    "    keys_e, values_e = digitize(norm_e, bin_count = bin_count)\n",
    "    keys, values = digitize(norm_x + norm_e, bin_count = bin_count)\n",
    "    interval = np.linspace(min(keys), max(keys), bin_count)\n",
    "    \n",
    "    norm = sps.norm.pdf(interval, 𝜇, 𝜎)\n",
    "    \n",
    "    kstest_result.append(sps.kstest(norm, values_x).pvalue)\n",
    "    \n",
    "    if debug:\n",
    "        plt.plot(interval, values_x, color = 'green')\n",
    "        plt.plot(interval, values_e, color = 'blue')\n",
    "        plt.plot(interval, values, color = 'red')\n",
    "        plt.show()\n",
    "\n",
    "plt.bar(range(1, size + 1), kstest_result)\n",
    "plt.show()\n",
    "\n",
    "print(\n",
    "    fr\"При пороге p-value в {critical}, {sum(x > critical for x in kstest_result)} из {size}\\\n",
    "    нулевых гипотез о нормальности полученного распределения не отвергнуто\"\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
